Theorems · Theorem · commutative algebra

fg_of_injective

∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {P : Type u_4} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module S P] [IsNoetherian S P]
  {N : Submodule R M} {σ : R →+* S} {σ' : S →+* R} [RingHomInvPair σ σ'] [RingHomInvPair σ' σ] (f : M →ₛₗ[σ] P),
  Function.Injective ⇑f → N.FG

Defined in

Mathlib.RingTheory.Noetherian.Basic

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleIsNoetherianRingHomInvPairRingHomInvPair